If Bitcoin is rewarded through mining, and mining is the process of packing some transactions in a block(and adding that block successfully to the blockchain), and on the other hand, a transaction itself is sending Bitcoins to someone else, then isn't this a chicken and egg issue? How could a transaction(say the first one) take place at all when there's no Bitcoin yet? Just getting myself familiar with the basic concepts of Bitcoin.

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A valid Bitcoin block has to include a minimum of one transaction, which is the coinbase transaction that pays out the block reward. Most of the early Bitcoin blocks did not include transactions that sent bitcoins from one party to other, but included only the coinbase transaction that paid out the newly minted bitcoins.

In fact, the first transaction wherein an exchange of coins occurred was in block #170, when Satoshi sent 10 BTC to Hal Finney